Answer:
M= 15 degrees N= 15 degrees
Step-by-step explanation:
Right triangles are always 90 degrees so 90-60=30
since theres 2 sides you have to split 30 in 2 so 30 divided by 2 equals 15
Answer:
(x²-10x+33)/(-8) = y
Step-by-step explanation:
The distance between any point on a parabola from both its focus and directrix are the same.
Let's say we have a point (x,y) on the parabola. We can then say that using the distance formula,
is the distance between (x,y) and the focus. Similarly, the distance between (x,y) and the directrix is |y-1| (I use absolute value here because distance is always positive). We can find this equation by taking the shortest distance from the point to the line. Because the closest point to the line will be the same x value as the point itself, the distance is simply the distance between the y value of the point and the y value of the directrix.
Equating the two equations given, we have

square both sides to get
(x-5)²+(y+3)²=(y-1)²
expand the y components
(x-5)² + y²+6y+9 = y²-2y+1
subtract y²+6y+9 from both sides
(x-5)² = -8y - 8
expand the x components
x²-10x+25 = -8y - 8
add 8 to both sides to isolate the -8y
x²-10x+33 = -8y
divide both sides by -8 to isolate y
(x²-10x+33)/(-8) = y
Answer:

Step-by-step explanation:
When does the value of f(x) = (1/2)x equal the value of g(x) =2x+8?

Answer:
x has no real solution
Step-by-step explanation:
Our equation is qudratic equation so the method we will follow to solve it is using the dicriminant :
- Let Δ be the dicriminant
- a=1
- b=2
- c=9
- Δ= 2²-4*1*9 =4-36=-32
- we notice that Δ≤0⇒x has no real solution